Answer:
What runs around all day. Then lies under the bed. With its tongue hanging out?
I run around the city, but I never move.
It is the assumed nocturnal symbol of Mr. Wayne. What is it?
I turn around once. What is out will not get in. I turn around again. What is in will not get out.
What grows in winter, dies in summer, and grows roots upward?
I have two eyes in the front and a lot of eyes on my tail